Why is ice cold water rather than room temperature or warm water used to wash the remainder of the benzoic acid out of the beaker?

As a general rule:

"Solubility of compounds decrease with the increasing of temperature" as you can see in the graph.

Also, filtration, is a chemical process where you are separating a precipitate from a solution.

Now, if you want to recover benzoic acid from an aqueous solution, the better option would be with Ice cold water because its solubility will be lower because temperature is lower producing more precipitate.

Learn more about this process in:

Ibelieve its a because an empirical formula usually has a ch in it your options are a or b

The activity series is shown in the attached picture. if the element is below the other, then you can displace the other. following the activity series as a guide, the reactions are as follows: nickel and aluminum chloride3 ni + 2 alcl₃  → 3 nicl₂ + 2 albarium and copper bromideba + cubr  →  no reaction because cu is less oxidizable than bapotassium nitrate and aluminum3 kno₃ + al  → al(no₃)₃ + 3 ksodium phosphate and zincnaso₄ + zn  → znso₄ + na